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    Darboux cyclides and webs from circles

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    Type
    Article
    Authors
    Pottmann, Helmut cc
    Shi, Ling
    Skopenkov, Mikhail
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Visual Computing Center (VCC)
    Computer Science Program
    Date
    2012-01
    Preprint Posting Date
    2011-06-07
    Permanent link to this record
    http://hdl.handle.net/10754/562040
    
    Metadata
    Show full item record
    Abstract
    Motivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order ≤4 are a superset of Dupin cyclides and quadrics, and they carry up to six real families of circles. Revisiting the classical approach to these surfaces based on the spherical model of 3D Möbius geometry, we provide computational tools for the identification of circle families on a given cyclide and for the direct design of those. In particular, we show that certain triples of circle families may be arranged as so-called hexagonal webs, and we provide a complete classification of all possible hexagonal webs of circles on Darboux cyclides. © 2011 Elsevier B.V. All rights reserved.
    Citation
    Pottmann, H., Shi, L., & Skopenkov, M. (2012). Darboux cyclides and webs from circles. Computer Aided Geometric Design, 29(1), 77–97. doi:10.1016/j.cagd.2011.10.002
    Publisher
    Elsevier BV
    Journal
    Computer Aided Geometric Design
    DOI
    10.1016/j.cagd.2011.10.002
    arXiv
    1106.1354
    Additional Links
    http://arxiv.org/abs/arXiv:1106.1354v1
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cagd.2011.10.002
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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